Four-parameter Equations Research Articles

Critical Period of Weed Control in Maize as Influenced by Soil Tillage Practices and Glyphosate Application

Increasing evidence on environmental and economic benefits has raised farmers’ interest in adopting alternative, less intensive soil management practices. To evaluate the influence of weed-competitive ability in response to a different tillage regime, a field study was conducted in maize under humid Central European climatic conditions in Slovenia. This study was established as a split-plot arrangement with three tillage practices (TPs) as the main plot: conventional (CN), conservation (CS), and no tillage (NT); this was combined with glyphosate application and the weed removal timing as the subplot. The weed removal timings were at the V3, V6, V9, V15, and R1 maize stages, with weed-free and weed season-long monitoring. The beginning and the end of the critical period of weed control (CPWC), based on a 5% maize yield loss rate, were determined by fitting the four-parameter log-logistic equations to the relative maize dry grain yield. The weed dry biomass from maize germination until the R1 growth stage in the NT TP was consistently lower than that in the CN and CS TP. Moreover, the NT TP resulted in a shorter CPWC (39 days after emergence (DAE)) compared to the CN (57 DAE) and CS (58 DAE). The results of CTWR (critical timing of weed removal) showed that less intensive tillage operations in the CS resulted in an earlier need for weed control (V2 and 23 DAE) compared to the CN (V3 and 39 DAE) and NT (V3 and 40 DAE). Our study suggests that the intensive tillage operations performed in the CN TP and the pre-sowing use of non-selective burndown herbicide in the NT delay the CTWR by more than 2 weeks, thus reducing the need for early post-emergence herbicide application in maize.

Comparison between the Four-parameter and Five-parameter Logistics Equations in the Determination of the Limits of Detection of Ochratoxin A

Ochratoxin A, a type of mycotoxin, was detected in plant sample matrices using the "optical waveguide lightmode spectroscopy" (OWLS) method. The calibration curve for the detection of ochratoxin A utilizing "optical waveguide lightmode spectroscopy" (OWLS) displayed a sigmoidal shape; hence, the 5-parameter logistics (5-PL) or 4-parameters logistics (4-PL) model should be used to fit the data rather than a linear model. Through the use of error function analysis and various functions such as Bias Factor, corrected Akaike Information Criterion (AICc), adjusted correlation coefficient (adjR2), Hannan–Quinn information criterion (HQC), Root Mean Square Error (RMSE), Bayesian Information Criterion (BIC), and Accuracy Factor, the distinction between the 5-PL and 4-PL models is found to be inconsistent. The half maximal effective concentration (EC50) confidence intervals overlapped, indicating no difference between the two methods; the 4-PL model was chosen because of its fewer parameters. The Limits of Detection (LOD) calculated using the 4-PL equation was 0.818 ng/mL, with a 95% confidence interval of 0.526-1.143 ng/mL. This value falls within the estimated range of 0.5 to 10 ng/mL found in the first investigation. Not only was the linear component of the data curve successfully represented by this study's use of the 4-PL model, but the model was also successful in representing the entire date curve.

The Critical Period of Weed Control Influences Sunflower (Helianthus annuus L.) Yield, Yield Components but Not Oil Content

Field studies were conducted in the northeastern part of the Republic of Croatia to determine the influence of the critical period of weed interference on sunflower (Helianthus annuus) yield, yield components, and oil content. For this purpose, different durations of competition were established, allowing weeds to infest the crop for increasing periods of time after planting or maintaining plots weed-free for increasing periods of time after planting. The beginning and the end of the critical period of weed control (CPWC), based on a 5% and 10% loss of sunflower yield, were determined by fitting the four-parameter log-logistic equations to the relative seed yield. The total weed biomass increased progressively in relation to the increase in the competition. The beginning of the CPWC period, based on a 5% acceptable yield loss, ranged from 141 to 234 growing degree days (GDD), which corresponded to the two-to-four true leaf development stage (the V2–V4 growth stages) across both sites and years. The crop had to be kept weed-free until a period when sunflower inflorescence began to open and flower (the R4–R5 growth stage) or from 1365 to 1932 GDD. The sunflower yield and yield components varied between the years and among locations. An increasing duration of weed interference negatively affected crop height, head diameter, and 1000-kernel weight, but not seed oil content.

A comparison of four common mathematical models to assess baroreflex sensitivity.

Different methods have been used to assess baroreflex gain in experiments where changes in the carotid sinus pressure or the arterial blood pressure using different techniques provoke a baroreflex response, usually a rapid variation of heart rate. Four mathematical models are most used in the literature: the linear regression, the piecewise regression, and two different four-parameter logistic equations: equation 1, Y = (A1-D1)/[1 + eB1(X - C1) ] + D1; equation 2, Y = (A2-D2)/[1 + (X/C2)B2 ] + D2. We compared the four models regarding the best fit to previously published data in all vertebrate classes. The linear regression had the worst fit in all cases. The piecewise regression generally exhibited a better fit than the linear regression, though it returned a similar fit when no breakpoints were found. The logistic equations showed the best fit among the tested models and were similar to each other. We demonstrate that equation 2 is asymmetric and the level of asymmetry is accentuated according to B2. This means that the baroreflex gain calculated when X = C2 is different from the actual maximum gain. Alternatively, the symmetric equation 1 returns the maximum gain when X = C1. Furthermore, the calculation of baroreflex gain using equation 2 disregards that baroreceptors may reset when individuals experience different mean arterial pressures. Finally, the asymmetry from equation 2 is a mathematical artifact inherently skewed to the left of C2, thus bearing no biological meaning. Therefore, we suggest that equation 1 should be used instead of equation 2.

Age and Sex Comparison of the Canine Supraspinatus Tendon Using Quantitative Magnetic Resonance Imaging T2 Mapping.

The normal canine supraspinatus tendon has properties commonly attributed to damage such as core hyperintensity and increased width. Little is published regarding the normal tendon, including how senescent changes and sex differences may affect the appearance. Conventional magnetic resonance imaging (MRI) techniques provide subjective analysis of tendons based on observer assessment of signal intensity and appearance. Quantitative MRI (qMRI) techniques such as T2 mapping provide an objective comparison of collagen orientation with analysis of a decay constant, T2. This study investigates age and sex related changes in the canine supraspinatus tendon using the qMRI technique of T2 mapping. In this study, 34 tendons of clinically sound male and female dogs (0.6-13 years) were imaged using qMRI T2 mapping techniques. Sagittal plane T2 maps of the supraspinatus tendon were depth-normalized, and profiles compared using two separate four-parameter logistic equations describing T2 mapping profiles as sigmoidal curves. Combined parameters evaluated included range of T2 values, curve steepness, vertical curve shift, lower bound of T2, upper bound of T2 and horizontal curve shift. A significant reduction in the most central portion of the supraspinatus tendon was found for every increased year in age (-1.56 ± 0.47 milliseconds [-2.56, -0.56, p = 0.004]). No significant difference in curve parameters was found between sexes. The reduction in T2 with age suggests a senescent change may be anticipated with the canine supraspinatus tendon.

Constitutive models that exceed the fitting capabilities of the Herschel–Bulkley model: A case study for shear magnetorheology

A significant proportion of non-Newtonian fluids exhibits the phenomena of shear-thinning and yield stress. The Herschel-Bulkley model is probably the most widespread equation to describe the rheological behaviour of such systems, although greater attention is being paid to discerning more accurate mathematical models for viscoplastic systems. In this regard, the work presented herein investigates existing, unconventional viscoplastic models and evaluates their fitting and predictive capabilities in relation to collected magnetorheological data. The four-parameter models of modified Carreau, modified Cross (and its variant extended with the Quemada equation), Shulman and Nasiri-Ashrafizadeh were applied to appraise the shear data of the magnetorheological fluids. Their suitability was also statistically evaluated and compared with that attained for the conventional Herschel-Bulkley model and recently employed analogues, such as the Robertson-Stiff and Mizrahi-Berk models. It was found that the performance of all models for describing magnetorheological flow curves was adequate, with relatively high correlation coefficients. Applying the four-parameter models, however, provided higher accuracy, demonstrated by notably reduced statistical coefficients of regression analysis. Both of the modified Carreau and Cross models exhibited superior fitting performance (up to 4-times lower root mean square error), while the Shulman and Nasiri-Ashrafizadeh models proved questionable in application. Although interpreting four-parameter equations is a rather complex matter, they provided more reliable prediction of shear stress data across the entire range of shear rate than the Herschel-Bulkley approximation, especially the modified Carreau and modified Cross models. It is believed that these findings can be extended to describe the rheology of other systems with viscoplastic characteristics.

Prediction of the hydrophobicity of platinum(IV) complexes based on molecular surface properties

A quantitative structure–property relationship (QSPR) study was performed for predicting the hydrophobicity of Pt(IV) complexes. Two four-parameter equations, one based solely on structural descriptors derived from electrostatic potentials (ESPs) on molecular surface, and the other integrated ESP descriptors with molecular surface area (AS), were firstly constructed. Mechanistic interpretations of the structural descriptors introduced were elucidated in terms of solute-solvent intermolecular interactions. Subsequently, several up-to-date modeling techniques, including support vector machine (SVM), least-squares support vector machine (LSSVM), random forest (RF) and Gaussian process (GP), were utilized to build the nonlinear models. Systematical validations including leave-one-out cross-validation, the validation for test set, as well as a more rigorous Monte Carlo cross-validation were performed to verify the reliability of the constructed models. The predictive performances of the four different nonlinear modeling methods follow the order of LSSVM≈GP > RF > SVM. The pure-ESP-based models are generally inferior to the AS-integrated ones. Comparisons with previous results were made.

A DFT study on recombination of alkyl radicals to C2-C17 normal alkanes & branched C8 alkanes and corresponding C-C bond pyrolysis reaction

Alkane C–C dissociation is one of the key elementary reactions in combustion and pyrolysis. Corresponding rate constants are important in kinetic models. However, reliable rate constants for long and branched alkanes are still limited, and accurate rate constant calculation for large alkanes is time-consuming. In this work we have systematically investigated the high-pressure-limit rate constants of alkyl recombination to normal CnH2n+2 (n=2–17) and some branched alkanes with UM06-2X/cc-pvdz//VRC-TST method.Corresponding dissociation rate constants have been converted using calculated free energies at G4MP2 level. This combined method is found to reproduce dissociation rate constants well (error < 101) for small alkanes at 700–2000 K. Our results suggested that it’s a good approximation to use short alkane (C3 for example) dissociation rate constants for longer alkanes above 800 K. Dissociation reactions leading to CH3 radical are much harder than those leading to other alkyls.It's a good approximation to use rate constant of dissociation leading to C2H5 radical for other alkyl dissociations other than CH3. Both modified and a four-parameter Arrhenius equations give good fitting to calculated rate constants. Our results give further insight into C–C bond dissociation of long and branched alkanes, and provide alternative kinetic data for relevant combustion/pyrolysis kinetic models.

Temperature and Wavelength Dependence of Effective Geometry Parameter and a Comparative Study of Orientational Order

Temperature and wavelength dependence of effective geometry parameter, the ratio of ordinary and extraordinary refractive indices, is reported. A modified four-parameter model and the Cauchy equations are opted to explain the temperature and wavelength dependence of effective geometry parameter, respectively. Additionally, the order parameter variation of effective geometry parameter is also studied. Influence of effective geometry parameter on the deflection of light by the liquid crystal compounds is also discussed. Different methods for the determination of order parameter from the optical data are compared. The order parameter is determined by using the birefringence, Vuks, and Neugebauer methods. The fitting results, obtained by the application of four-parameter model and Cauchy equations, are validated using the experimental data available in literature. A fine agreement is obtained between the experimental data and fitting results.

Optimization of the separation of chlorophenols with stepwise gradient elution in reversed phase liquid chromatography

An optimization technique based on gradient elution was used to separate eleven chlorophenols by reversed phase liquid chromatography. The separation was based on gradient elution with a stepwise variation pattern of the volume fraction of organic modifier, phi, in the mobile phase. Initially, two-, three-, and four-parameter equations which describe the dependence of ln k' upon phi, were examined for their ability to fit the experimental data. It was found that, among these equations, the four-parameter equation gave the best fit of the experimental data. In addition to separation optimization, a non-linear least squares program with a grid search for initial estimates was used to determine the best variation pattern. The best variation pattern was obtained with phi(1)= 0.27, phi(2)= 0.39, phi(3)= 0.62, t(1) = 33 min, and t(2) = 11 min. This pattern allowed the chromatographic separation of the chlorophenols with a good resolution and a total analysis time of 51 min. Good agreement was observed between predicted and experimental values of the retention times under optimal condition.

Comparative study of the performance of three- and four-parameter correlation equations for the temperature dependence of the enthalpy of vaporization for pure substance refrigerants

A few commonly used correlation equations of the enthalpy of vaporization which is essential to the analysis of refrigeration cycles are reviewed. A new four-parameter correlation equation is proposed assuming that the enthalpy of vaporization could be represented by a function having a linear term to the temperature and an additional term which slowly decreases as the temperature increases. It is not a common practice to measure the enthalpy of vaporization by experiment; therefore, performance of the new correlation equation for the temperature dependence of the enthalpy of vaporization is examined using numeric data from the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) tables for 22 pure substance refrigerants. The new correlation equation and other existing ones are fitted to the data optimizing the root mean squared deviation. All data points are weighted equally and NBP (normal boiling point) is used as a fixed point since the NBP is important for refrigeration applications. The new four-parameter equation yields an average absolute deviation of 0.05% for 22 refrigerants which is smaller than those of other four-parameter equations, such as Guermouche–Vergaund (0.08%), Aerebrot (0.13%), Radoz–Lyderson (0.08%), and Somayajulu four-parameter equation (0.08%). After the optimization, it is found that a specific exponent in the new equation has approximately the same value for almost every substance tested so that the original four-parameter correlation could be reduced to a three-parameter one. The new three parameter correlation yields an average absolute deviation of 0.14% for the same 22 refrigerants, which also is smaller than those of other three-parameter correlations, such as Xiang (0.18%), Majer–Svoboda–Pick (0.18%), and Somayajulu three-parameter equation (0.27%).

Use of RP-TLC to investigate the solubility in water of fatty acids, hydroxy fatty acids and their esters

Long-chain fatty acids and hydroxy fatty acids and their esters have been separated by reversed-phase thin-layer chromatography with three mobile phases. New methods for calculation of the solubility in water (log W ) from experimental R M values and other physicochemical data have been proposed. The most accurate prediction of log W values of the acids and esters was achieved by use of four-parameter equations relating the R M values of the compounds, the numerical values of the Pyka topological index ( 0 B ), the electrotopological states of oxygen atoms of the carbonyl groups ( E 01 ) or of the oxygen atoms of hydroxyl groups ( E 02 ), and the dipole moments (μ ppm ) of the mobile phases.

Momentum transfer in an agitated vessel with off-centred impellers

AbstractMomentum transfer was investigated in an unbaffled agitated vessel of inner diameter 0.3 m equipped with different off-centred impellers. The distribution of the shear rate on the tank wall as a function of the impeller type and Reynolds number was studied in the turbulent regime of the Newtonian liquid flow. The dependences of the averaged dimensionless shear rate, friction coefficient, and dissipated energy on the Reynolds number and eccentricity ratio were approximated using four-parameter equations.

Previtamin D3 with a trans-Fused Decalin CD-ring Has Pronounced Genomic Activity

Deletion of C19 in the structure of 1 alpha,25-dihydroxyvitamin D3 [1,25(OH)2D3] does not substantially alter the biological potency but prevents the conversion between the vitamin and the previtamin form. Hence, this modification allows the study of locked previtamin and vitamin forms. The locked 19-nor-1,25(OH)2-previtamin D3 analog (19-nor-previtamin D) had a low biological activity and was a rather weak activator of the genomic signal transduction pathway. 19-Nor-trans-decalin-1,25(OH)2-vitamin D3 (19-nor-TD-vitamin D), characterized by the presence of a trans-fused decalin CD-ring system, was 10-fold more potent than the parent compound and was a potent activator of the genomic signal transduction pathway. Surprisingly, the previtamin, 19-nor-trans-decalin-1,25(OH)2-previtamin D3 (19-nor-TD-previtamin D), was as potent as 1,25(OH)2D3 in inhibiting cell proliferation and inducing cell differentiation and represents the first previtamin structure with pronounced vitamin D-like activity. Furthermore, this compound interacted as efficiently as 1,25(OH)2D3 with the vitamin D receptor (VDR), retinoid X receptor (RXR), coactivators, and DNA, which illustrated its potent ability to activate the genomic signal transduction pathway. Analysis of the transactivation potency of 12 VDR point mutants after stimulation with 19-nor-TD-previtamin D revealed that this analog used the same contact points within the receptor as did 1,25(OH)2D3. This could be confirmed by modeling analysis of this compound in the ligand binding pocket of VDR. In conclusion, a previtamin D3 analog is presented with genomic activities equivalent to 1,25(OH)2D3.

The use of topological indexes to predict theRMvalues of higher fatty acids, hydroxy fatty acids, and their esters in RPTLC

Higher fatty acids and hydroxy fatty acids and their esters have been separated by reversed-phase thin-layer chromatography with three mobile phases. The R M values of the compounds have been correlated with the numerical values of topological indexes, with the electrotopological states of the atoms attached to the carboxyl group of the compounds, with the number of hydrogen-bond donors (#HD), with the molecular weights ( M W ) of the compounds, and with the dipole moments (µ mph ) of the mobile phases. The most accurate prediction of the R M values of the acids and esters, for all the mobile phases investigated, was achieved by use of four-parameter equations relating the dipole moments of the mobile phases to three other parameters.

Distribution Coefficient of β-Carotene in Systems Composed of Hexane, Water, and 2-Propanone and Toluene, Water, and 2-Propanone

The distribution coefficient of β-carotene between water and a mixed organic solvent was measured at T = 298.15 K. Binary solvent systems formed by 2-propanone with either hexane or toluene were used as the mixed solvent. The liquid−liquid equilibria (LLE), along with the tie lines, were determined for two ternary aqueous systems, hexane + water + 2-propanone and toluene + water + 2-propanone. These systems exhibit a parabolic miscibility gap. The coexistence curves were measured by a titration method, and results were smoothed by means of either three- or four-parameter equations.

Distribution Coefficient of β-Carotene in Systems Composed of Cyclohexane, Water, and 2-Propanone and Methylcyclohexane, Water, and 2-Propanone

The distribution coefficient of β-carotene between water and a mixed organic solvent was measured at T = 298.15 K. Binary solvent systems formed by 2-propanone with either cyclohexane or methylcyclohexane were used as the mixed solvent. The liquid−liquid equilibria, along with the tie lines, were determined for two ternary aqueous systems, viz., cyclohexane + water + 2-propanone and methylcyclohexane + water + 2-propanone. The systems exhibit a parabolic type miscibility gap. The coexistence curves were measured by the titration method, and results were smoothed by means of either three- or four-parameter equations.

Refractive Indices of the Optically Nonlinear Organic Crystal (S)-3-Methyl-5-nitro-N-(1-phenylethyl)-2-pyridinamine

The refractive indices of structurally well-characterized crystals of the new optically nonlinear organic crystal (S)-3-methyl-5-nitro-N-(1-phenylethyl)-2-pyridinamine have been measured from 480 to 660 nm and fitted to four-parameter Sellmeier equations with an accuracy of ±3 × 10-3 to ±5 × 10-3. The value of ny was accurately verified by the measurement of the external angle of incidence required, at the (101) plane, to observe type I phase matching with a fundamental wavelength of 1064 nm. The phase matching locus has been established and is of Hobden class eight. The values of the nx, ny, and nz refractive indices at 532 nm were found from the Sellmeier equations to be 1.690, 1.901, and 1.725, respectively, and their relative magnitudes are correlated with the molecular arrangement in the crystal lattice. This material is a member of a series of pyridinamines that can exhibit the phenomenon of frequency-dependent orientation of their dielectric axes. Since this compound crystallizes in an orthorhombic structure, rotation of the dielectric axes is precluded for symmetry reasons.

The birefringence of the optically nonlinear crystal 4-amino benzophenone

A precise method is presented for measuring the refractive index of an anisotropic prism with light polarized orthogonal to the prism axis which is also a dielectric axis. Prisms have been cut from crystals of the optically nonlinear 4-amino benzophenone with exceptionally low defect concentration as identified by synchrotron white light topography. The linear refractive indices of these have been measured and fitted to four-parameter Sellmeier equations to an accuracy of 7×10−6–3×10−3. The values are accurately verified by observation of the external angle of incidence to a (001) plane required to meet the conditions of type-I phase matching with a fundamental wavelength of 1064 nm. The phase matching is of Hobden class six for this wavelength. In common with similar organic molecular materials, the molecular charge transfer axis defines the most polarizable direction in the crystal, with the C=O direction being much less significant.

Chromatographic behaviour of phenylurea pesticides in high-performance liquid chromatography with nitrile- and amino-bonded stationary phases

The retention of phenylurea pesticides on nitrile- and amino-bonded stationary phases was measured over a broad composition range of 2-propanol— n-hexane and 2-propanol—water mobile phases. Minima of retention were observed on the nitrile phase in mobile phases containing 80–90% 2-propanol in water. In organic mobile phases, the plots of log k′ versus the concentration of 2-propanol in n-hexane are significantly curved. This behaviour can be attributed to combined effects of polar and hydrophobic interactions as the driving force of the retention. Simple two-parameter equations can be used to first-approximation description of retention on the nitrile bonded phase in mobile phases containing up to 50–60% 2-propanol in water and on the two bonded phases in mobile phases containing up to 60–80% 2-propanol in n-hexane. Four-parameter equations taking into account mixed mechanism of retention involving polar and hydrophobic interactions can be used to describe the retention of phenylurea compounds over the whole composition range of organic and aqueous—organic mobile phases and to allow prediction of retention and optimization of separation. The retention of phenylurea pesticides on the amino-bonded phase in mobile phase containing 2-propanol in water is too low to allow chromatographic separation of the compounds tested. The retention in aqueous—organic mobile phases is higher on the nitrile- than on the amino-bonded phase, but the selectivity of separation is unsatisfactory for most phenylurea pesticides. Most compounds tested can be separated in 2-propanol— n-hexane mobile phases, but significant differences in selectivities and even in the order of elution were observed between the two bonded phases.